1/4 of a sine wave as a control shape

The cycle~ object uses a lookup table of 512 values that make the shape of a single cycle of a cosine wave, and it reads through those repeatedly at whatever rate is specified in its left (frequency) inlet. You can also set the cycle~ to 0 Hz (its default frequency) and select a point in the cosine waveform with a value (either a signal or a float) from 0 to 1 in the right (phase offset) inlet. Thus, you can get a sinusoidal shaped signal (or any part of one) any time you want by sending the appropriate lookup values in the right inlet of cycle~.

This patch shows an example of using one fourth of a sinusoid to make a control shape. The line~ object sends a signal that goes linearly from 0.25 to 0.5 in 10 seconds. Since that signal is used as the lookup index in the cosine wavetable, cycle~ sends out a signal that goes from 0 to -1 in the shape of the second fourth of the wavetable. That 0 to -1 signal is scaled into the pitch range 96 to 72 (in MIDI-style values), resulting in a 2-octave change in the center frequency of the resonant bandpass filter (reson~) with a slowing curve easing it into the arrival pitch.